基于混沌与门限方案的图像加密方法研究

发布时间：2018-07-03 11:28

本文选题：中国剩余定理 + 分段线性函数　；参考：《西南大学》2017年硕士论文

【摘要】：随着计算智能的快速发展,图像所携带敏感信息的安全性越来越备受人们的关注。因此,图像加密算法也逐渐成为信息安全领域研究的热点问题。近几年,利用混沌特性对图像进行加密的算法也越来越完善。非线性系统参数取特定的值时,其动力学行为会非常依赖初始值的变化,而且迭代轨道不可精确预测。因此,该特性可以更好的应用到密码学中的扩散和混乱过程。此外,混沌系统的数学方程是确定的,只需要保障混沌参数和初始值的安全性,就可以重构出混沌序列。基于混沌的图像保护方法包括两方面,一方面是利用离散形式的混沌系统来迭代生成混沌序列,来改变图像像素的布局与替换像素灰度值,从而达到加密的效果;另一方面是基于混沌与门限方案的图像共享技术,通过多人合作来恢复原始图像,即使部分图像份额丢失,仍可重构出原始图像。论文对基于分段线性函数的图像编码与解码进行了比较深入的探讨,研究了基于图像块的分段线性函数的构造,并分析了其混沌特性。将基于信息熵的压缩编码与中国剩余定理(CRT)结合,可以有效地减小影子图尺寸,即改善影子图的数据膨胀问题。论文中将原始图像分割成若干个小的图像方块,统计每个图像块中不同的像素值所占比重,经过换算转化成概率分布,进而利用概率来构造分段线性区间及其对应的分段线性函数。然后,利用分段线性函数及其逆函数对分块图像进行解码与编码。由于每个图像块最终编码长度不一定相等,需要对最终所有图像块的编码进行分组处理,保证每组包含相同长度的二进制位。将二进制序列转化成对应的十进制,即待共享的密值。为了提高影子图对原始图像像素改变的敏感性,利用混沌序列对密值序列进行置乱处理。当改变块图像中像素值时,其对应的熵值亦会改变。如果其未发生变化,则生成一个小随机数叠加到该熵值上。然后,将所有块图像中的熵值构成一个集合,计算该集合的方差,作为Logistic映射进入混沌状态时迭代的起始点,能够得到不同的迭代轨道。用其对密值序列重新排序,能达到较好的抵抗差分攻击的效果。最后,利用CRT构建门限共享方案,将置乱后的密值序列转化成对应的影子图,分发给若干位合法的参与成员。此外,论文中分析了参与成员数量发生变化,即授权子集中包含新增成员。改进算法可以确保原有的参与成员手中的份额不变,通过与新增成员合作仍可以恢复出共享密值。为了保障共享方案的安全性,防止参与成员之间出现欺骗行为。论文设计了基于非对称密码的身份认证方案,只有通过验证的参与成员,才能利用各自独立拥有的密值份额,相互合作恢复出共享密值。通过计算机的数值仿真,并分析影子图的安全性相关判定指标,可以发现实验结果均符合理论要求,说明论文中所提出的方案对于密图共享是安全有效的。
[Abstract]:With the rapid development of computing intelligence, people pay more and more attention to the security of sensitive information carried by images. Therefore, image encryption algorithm has gradually become a hot issue in the field of information security. In recent years, the algorithm of image encryption based on chaos is becoming more and more perfect. When the parameters of the nonlinear system are given a certain value, the dynamic behavior of the nonlinear system depends very much on the change of the initial value, and the iterative orbit can not be predicted accurately. Therefore, this feature can be better applied to the diffusion and confusion of cryptography. In addition, the mathematical equations of chaotic systems are determined, and chaotic sequences can be reconstructed only by ensuring the security of chaotic parameters and initial values. The method of image protection based on chaos includes two aspects. On the one hand, chaotic sequences are generated iteratively by discrete chaotic system to change the layout of image pixels and replace the gray values of pixels so as to achieve the effect of encryption. On the other hand, the image sharing technology based on chaos and threshold scheme is used to restore the original image through multi-person cooperation. Even if part of the image is lost, the original image can still be reconstructed. In this paper, the image coding and decoding based on piecewise linear function are deeply discussed, and the construction of piecewise linear function based on image block is studied, and its chaotic characteristics are analyzed. Combining the compression coding based on information entropy with the Chinese residue Theorem (CRT), the size of shadow graph can be reduced effectively, that is, the problem of data expansion of shadow graph can be improved. In this paper, the original image is divided into several small image blocks, the proportion of different pixel values in each image block is counted, and the probability distribution is transformed by conversion. Then the piecewise linear interval and its corresponding piecewise linear function are constructed by probability. Then, the piecewise linear function and its inverse function are used to decode and encode the block image. Because the final coding length of each image block is not necessarily equal, it is necessary to block the coding of all the final image blocks to ensure that each group contains binary bits of the same length. Converts the binary sequence to the corresponding decimal value, the secret value to be shared. In order to improve the sensitivity of shadow image to the pixel change of the original image, chaotic sequence is used to scramble the dense sequence. When the pixel value in the block image is changed, the corresponding entropy value also changes. If it does not change, a small random number is generated and superimposed on the entropy value. Then the entropy values in all block images are formed into a set and the variance of the set is calculated as the starting point of the iteration when the Logistic map enters the chaotic state different iterative orbits can be obtained. It can be used to reorder the dense sequence, which can resist the differential attack. Finally, the threshold sharing scheme is constructed by using CRT, and the scrambled secret value sequence is transformed into the corresponding shadow graph, which is distributed to a number of legitimate participating members. In addition, the paper analyzes the changes in the number of participating members, that is, the authorized subset contains new members. The improved algorithm can ensure that the original share of the participating members remains unchanged, and can recover the shared secret value by cooperating with the new members. In order to ensure the security of the shared scheme and prevent cheating among the participating members. In this paper, an identity authentication scheme based on asymmetric cryptography is designed. Only by authenticating the participating members, can they recover the shared secret value by using their independent secret value shares. Through the numerical simulation of the computer and the analysis of the security index of the shadow graph, it can be found that the experimental results are all in line with the theoretical requirements. It is shown that the scheme proposed in this paper is safe and effective for the secret graph sharing.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP309.7

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